Tensor completion via nonconvex tensor ring rank minimization with guaranteed convergence

no code implementations • 14 May 2020 • Meng Ding, Ting-Zhu Huang, Xi-Le Zhao, Tian-Hui Ma

Key words: nonconvex optimization, tensor ring rank, logdet function, tensor completion, alternating direction method of multipliers.

Tensor train rank minimization with nonlocal self-similarity for tensor completion

no code implementations • 29 Apr 2020 • Meng Ding, Ting-Zhu Huang, Xi-Le Zhao, Michael K. Ng, Tian-Hui Ma

The TT rank minimization accompany with \emph{ket augmentation}, which transforms a lower-order tensor (e. g., visual data) into a higher-order tensor, suffers from serious block-artifacts.

Tensor N-tubal rank and its convex relaxation for low-rank tensor recovery

no code implementations • 3 Dec 2018 • Yu-Bang Zheng, Ting-Zhu Huang, Xi-Le Zhao, Tai-Xiang Jiang, Teng-Yu Ji, Tian-Hui Ma

Based on it, we define a novel tensor rank, the tensor $N$-tubal rank, as a vector whose elements contain the tubal rank of all mode-$k_1k_2$ unfolding tensors, to depict the correlations along different modes.